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Examples of Algebra Word Problems to practice at home.
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AGE PROBLEMS
PROBLEM #1 A boy is one-third as old as his brother and 8 years younger than his sister. The sum of their ages is 38 years. How old is each of them?
Let
x = age of boy
3x=age of brother
x+8= age of sister
x+3x+(x+8)=38
5x=30
x=6 years (age of boy)
3x=18 years(age of brother)
x+8=14years(ageof sister)
PROBLEM #2 Maria is 12 years older than her sister Josie. Six years ago, Maria was four times as old as Josie. Find their ages now.
Let
x=age of Josie now
x+12=age of Maria now
(x-6) and (x+6) are their respective ages 6 years ago.
x+6=4(x-6)
X=10 (age of Josie now)
x+12=22 years(age of Maria now)
Josie
Maria
PROBLEM #3 Eight years ago, Manny was three times as old as Ronnie. Now he is only twice as old as Ronnie. Find their ages now.
Let
x=Ronnies age 8 years ago
3x=Mannys age 8 years ago
x+8=Ronnies age now
3x+8=Mannys age now
3x+8=2(x+8)
X=8
3x=24
Ronnies age now=x+8=16 years
Mannys age now=3x+8=32 yeas
WORK PROBLEMS
PROBLEM #1 In what time wold A, B, and C together do a piece of job if A alone could do it in 6 hours more, B alone in 1 hour more, and C alone in twice the time?
PROBLEM #2 A can do a job in 8 days, and A and B can do the job together in 3 days. How long would it take B to do the job alone?
PROBLEM #3 One pipe can fill a tank alone in 6 hours; another pipe can fill it alone in 12 hours. If the tank is empty, and all three pipes are open, how long will it take to fill the tank?
NUMBER PROBLEMS
Let
x=the reqired number
x-3=the excess of the number over 3.
PROBLEM #2 The escess of the sum of the forth and fifth parts over the difference of the half and third parts of a number is 119. Find the number.
Let x= the required number
PROBLEM #3 The difference between two numbers is 24 and their sum is 60. Find the numbers.
Let x=one number
x+24= the other nmbers
x+(x+24)=60
2x=36
x=18
x=18
x+24=(18+24)=42
The numbers are 18 and 42.
PROBLEM #4 Find two consecutive odd numbers such that thrice the smaller number exceeds the larger by 12.
Let x=smaller odd number
x+2=larger odd number
3x-(x+2)=12
2x=14
x=7
x=7
x+2=(7+2)=9
The odd numbers are 7 and 9.
PROBLEM #5 Find two consecutive positive even numbers such that the difference of their squares is 76.
Let x=smaller positive even number
x+2=the larger positive even number
The even integers are 18 and 20.
MIXTURE PROBLEMS
PROBLEM #1 A goldsmith has two alloys of gold, the first being 70% pure gold, and the second 60% pure gold. How many grams of each must be used to make 100g of an alloy which will be 66% pure gold?
Let x=weight in g of the 70% pure gold
100-x=weight in g of the 60% pure gold
0.70x=actual gold in 70% alloy
0.60(100-x)=actual gold in 60% alloy
0.66(100)=actual gold in 66% alloy
100-x=100-60=40 grams
Therefore, there are 60g of 70% alloy and 40g of 60% alloy.
PROBLEM #2 A chemist has two alcohol solutions of different strengths, 30% alcohol and 45% alcohol solutions, respectively. How many cubic cm of each must be sed so as to make a mixture of 30 cubic cm which will contain 39% alcohol?
Let x=volume of 30% alcohol solution
30-x=volume of 45% alcohol solution
x=12cubic cm (30% alcohol solution)
30-x=30-12=18cubic cm (45% alcohol solution)
PROBLEM #3 Determine how much water should be evaporated from 50kg of a 30% salt solution to produce a 60% salt solution. All percentages are by weight.
Let x=weight of water in kg to be evaporated
Since the amount of salt remains in the solution, we havce
Weight of salt in 30% solution=weight of salt in 60% solution
PROBLEM #4 How many liters of 45% alcohol solution must be added to 60 liters of a 15% alcohol solution to obtain a 25% alcohol solution?
Let x=number of liters of 45% alcohol solution to be added
x+60=volume in liters of the mixture
Alcohol in 45% solutiion+alcohol in 15% solution=alcohol in 25% solution
PROBLEM #5 Rice worth P15 per kg is to be mixed with rice worth P20 per kg to make up 50kg of a mixture to sell at P18 per kg. Determine the weight of each kind of rice in the mixture.
Let x=the number of kg of rice worth P15/kg
50-x=the number of kg of rice worth P20/kg
Value of P15/kg rice + value of P20/kg rice = value of mixture
x=20 kg (weight of P15/kg rice)
50-x=50-20=30kg (weight of P20/kg rice)
MOTION PROBLEMS
PROBLEM #1 A runs around a circular track in 60sec, and B in 50sec. Five seconds after A starts, B starts from the same point in the same direction. When will they be together for the first time, assming they run around the track continuously?
Let C= circumference of the track
t=time when A and B will be together for the first time, reckoned from the time A started
t-5=time of B
A and B will be together when the difference between the disctance run is one circumference. Hence
PROBLEM #2 Two cars A and B, with average speeds of 40 and 50km/hr, respectively, are 220km apart. Car A starts a 8am toward B, while N starts at 9am toward A. At what time will they meet?
Let t=hours A will travel before meeting B
t-1=hours will travel before meeting A
Distance travelled by A= 40t km
Distance travelled by B=50(t-1)km
40t+50(t-1)=220
40t+50t-50=220
90t=270
t=3 hours
8am+3hours=11am
PROBLEM #3 A man started on his bicycle for Manila, a distance of 30km intenting to arrice at a certain time. After riding 10km he was detained for half an hour, and as a result he was obliged to ride the rest of the way 2km/hr faster. What was his original speed?
v=8km/hr (original speed)
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